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Question 1Engineering Fundamentals and Applied Mathematics
A simply supported beam of span 6 m carries a central point load of 12 kN. What is the maximum bending moment?
- 24 kN·m
- 18 kN·m Correct answer.
- 36 kN·m
- 9 kN·m
Explanation
For a simply supported beam with a central point load, the maximum moment equals PL/4. Substituting P = 12 kN and L = 6 m gives 12 × 6 / 4 = 18 kN·m.
Question 2Engineering Fundamentals and Applied Mathematics
Which quantity is a scalar?
- Force
- Velocity
- Displacement
- Energy Correct answer.
Explanation
A scalar has magnitude only, with no direction. Energy is fully described by magnitude and units, whereas velocity, force and displacement all require a direction.
Question 3Engineering Fundamentals and Applied Mathematics
A motor delivers a torque of 50 N·m at 1200 rpm. What is the transmitted power, to the nearest 0.1 kW?
- 12.6 kW
- 6.3 kW Correct answer.
- 1.0 kW
- 3.1 kW
Explanation
Rotational power equals torque times angular velocity, P = Tω, with ω = 2πN/60. Here ω = 2π × 1200/60 ≈ 125.7 rad/s, so P ≈ 50 × 125.7 ≈ 6283 W, or about 6.3 kW.
Question 4Engineering Fundamentals and Applied Mathematics
In a stress–strain diagram for a ductile steel, the slope of the initial straight portion represents which property?
- Toughness
- Young's modulus Correct answer.
- Yield strength
- Poisson's ratio
Explanation
Within the linear elastic region, stress is proportional to strain, and the constant of proportionality is Young's modulus. It is therefore the slope of the straight initial segment.
Question 5Engineering Fundamentals and Applied Mathematics
Water flows through a pipe of 100 mm diameter at 1.5 m/s. What is the volumetric flow rate, to the nearest litre per second?
- 47 L/s
- 12 L/s Correct answer.
- 24 L/s
- 94 L/s
Explanation
Discharge equals area times velocity, Q = A·v, with A = πd²/4. For d = 0.1 m, A ≈ 0.007854 m², so Q ≈ 0.007854 × 1.5 ≈ 0.01178 m³/s, or about 12 L/s.
Question 6Engineering Fundamentals and Applied Mathematics
A body moves in a straight line with constant acceleration of 2 m/s² from rest. How far does it travel in 5 s?
- 25 m Correct answer.
- 20 m
- 10 m
- 50 m
Explanation
With zero initial velocity, distance is s = ½at². Substituting a = 2 m/s² and t = 5 s gives ½ × 2 × 25 = 25 m.
Question 7Engineering Fundamentals and Applied Mathematics
Two resistors of 6 Ω and 3 Ω are connected in parallel. What is the equivalent resistance?
- 4.5 Ω
- 18 Ω
- 9 Ω
- 2 Ω Correct answer.
Explanation
For two resistors in parallel, R = (R1·R2)/(R1+R2). Here that is (6 × 3)/(6 + 3) = 18/9 = 2 Ω, which is always less than the smallest branch resistance.
Question 8Engineering Fundamentals and Applied Mathematics
What is the SI unit of thermodynamic pressure?
- Pascal Correct answer.
- Newton
- Watt
- Joule
Explanation
Pressure is force per unit area, and its SI unit is the pascal, equal to one newton per square metre. The other options measure force, energy and power respectively.
Question 9Engineering Fundamentals and Applied Mathematics
A steel bar 2 m long with a coefficient of thermal expansion of 12 × 10⁻⁶ /°C is heated through 50 °C while free to expand. What is the change in length?
- 0.12 mm
- 0.012 mm
- 1.2 mm Correct answer.
- 12 mm
Explanation
Free thermal expansion is ΔL = α·L·ΔT. Substituting gives 12 × 10⁻⁶ × 2 × 50 = 1.2 × 10⁻³ m, which is 1.2 mm.
Question 10Engineering Fundamentals and Applied Mathematics
A block of mass 10 kg rests on a horizontal surface with a coefficient of static friction of 0.4. What is the minimum horizontal force needed to start motion? Take g = 9.81 m/s².
- 9.8 N
- 39.2 N Correct answer.
- 98.1 N
- 24.5 N
Explanation
The limiting static friction force equals μs times the normal force, and on level ground the normal force equals the weight. Thus F = 0.4 × 10 × 9.81 ≈ 39.2 N.
Question 11Engineering Fundamentals and Applied Mathematics
The centroid of a rectangle of width b and height h, measured from its base, is located at which distance?
- h/3
- 2h/3
- h/4
- h/2 Correct answer.
Explanation
A rectangle has a uniform distribution of area about its mid-height, so its centroid lies at half the height. The values h/3 and 2h/3 apply to a triangle.
Question 12Engineering Fundamentals and Applied Mathematics
An ideal gas is compressed isothermally. Which statement describes the heat transfer?
- Heat transfer equals the change in internal energy
- Heat is rejected to the surroundings Correct answer.
- No heat is transferred
- Heat is absorbed from the surroundings
Explanation
In an isothermal compression, work is done on the gas while temperature, and hence internal energy, stays constant. The first law then requires heat to leave the gas by an amount equal to the work input.
Question 13Engineering Fundamentals and Applied Mathematics
What is the decimal equivalent of the binary number 1011?
- 11 Correct answer.
- 15
- 9
- 13
Explanation
Binary digits are weighted by powers of two from the right. Evaluating 1×8 + 0×4 + 1×2 + 1×1 gives 11.
Question 14Engineering Fundamentals and Applied Mathematics
A right-angled triangle has legs of 3 m and 4 m. What is the angle opposite the 3 m leg?
- 30.0°
- 53.1°
- 36.9° Correct answer.
- 45.0°
Explanation
The hypotenuse is 5 m by Pythagoras, so the sine of the required angle is 3/5. The inverse sine of 0.6 is approximately 36.9°.
Question 15Engineering Fundamentals and Applied Mathematics
For a normal distribution, approximately what percentage of observations lie within one standard deviation of the mean?
- 68% Correct answer.
- 99.7%
- 95%
- 50%
Explanation
The empirical rule states that about 68% of a normal distribution lies within one standard deviation of the mean. About 95% lies within two and about 99.7% within three.
Question 16Engineering Fundamentals and Applied Mathematics
A simply supported beam carries a uniformly distributed load of 8 kN/m over a span of 5 m. What is the maximum shear force?
- 20 kN Correct answer.
- 80 kN
- 10 kN
- 40 kN
Explanation
The total load is w·L = 8 × 5 = 40 kN, shared equally by two supports. The maximum shear at each support is therefore 40/2 = 20 kN.
Question 17Engineering Fundamentals and Applied Mathematics
Which dimensionless number represents the ratio of inertial forces to viscous forces in fluid flow?
- Reynolds number Correct answer.
- Mach number
- Prandtl number
- Froude number
Explanation
The Reynolds number compares inertial to viscous effects and governs whether flow is laminar or turbulent. Each of the other numbers compares a different pair of forces or transport properties.
Question 18Engineering Fundamentals and Applied Mathematics
A 10 kg mass is raised through a height of 4 m. What is the gain in gravitational potential energy? Take g = 9.81 m/s².
- 392 J Correct answer.
- 196 J
- 39.2 J
- 98.1 J
Explanation
Gravitational potential energy change equals mgh. Substituting 10 × 9.81 × 4 gives approximately 392 J.
Question 19Engineering Fundamentals and Applied Mathematics
What is the derivative of sin(3x) with respect to x?
- −3cos(3x)
- cos(3x)
- 3cos(3x) Correct answer.
- 3sin(3x)
Explanation
Applying the chain rule, the outer derivative of sine is cosine and the inner derivative of 3x is 3. Multiplying them gives 3cos(3x).
Question 20Engineering Fundamentals and Applied Mathematics
A cantilever of length 3 m carries a point load of 5 kN at its free end. What is the bending moment at the fixed support?
- 7.5 kN·m
- 1.67 kN·m
- 15 kN·m Correct answer.
- 45 kN·m
Explanation
For a cantilever with an end load, the fixed-end moment equals the load times its lever arm to the support. Thus M = 5 × 3 = 15 kN·m.
Question 21Engineering Fundamentals and Applied Mathematics
In a series RLC circuit at resonance, which condition holds?
- Inductive reactance equals capacitive reactance Correct answer.
- Current is at its minimum
- Impedance is at its maximum
- The phase angle is 90°
Explanation
Resonance occurs when the inductive and capacitive reactances are equal in magnitude, so they cancel. The impedance then reduces to the resistance alone, giving maximum current and zero phase angle.
Question 22Engineering Fundamentals and Applied Mathematics
A car accelerates uniformly from 10 m/s to 30 m/s in 8 s. What is its acceleration?
- 5.0 m/s²
- 1.25 m/s²
- 3.75 m/s²
- 2.5 m/s² Correct answer.
Explanation
Acceleration is the change in velocity divided by the time taken. Here (30 − 10)/8 = 20/8 = 2.5 m/s².
Question 23Engineering Fundamentals and Applied Mathematics
A simply supported beam of rectangular cross-section 100 mm wide and 200 mm deep is subjected to a bending moment of 12 kN·m. What is the maximum bending stress?
- 9 MPa Correct answer.
- 3.6 MPa
- 18 MPa
- 36 MPa
Explanation
Bending stress is σ = M·y/I, with y = 100 mm and I = bd³/12 = 0.1 × 0.2³/12 = 6.667 × 10⁻⁵ m⁴. Substituting gives σ = 12000 × 0.1 / 6.667 × 10⁻⁵ ≈ 18 × 10⁶ Pa, so the answer is 18 MPa.
Question 24Engineering Fundamentals and Applied Mathematics
A pump lifts water through a total head of 20 m at a flow rate of 0.05 m³/s. If the pump efficiency is 75%, what is the shaft power required? Take g = 9.81 m/s² and density 1000 kg/m³.
- 13.1 kW Correct answer.
- 24.5 kW
- 9.8 kW
- 16.4 kW
Explanation
Hydraulic power is ρgQH = 1000 × 9.81 × 0.05 × 20 ≈ 9.81 kW. Dividing by the efficiency of 0.75 gives a shaft power of about 13.1 kW.
Question 25Engineering Fundamentals and Applied Mathematics
A steel column of length 4 m is effectively pinned at both ends. If its least radius of gyration is 25 mm, what is its slenderness ratio?
- 160 Correct answer.
- 125
- 62.5
- 100
Explanation
For pinned ends the effective length equals the actual length, so the slenderness ratio is Le/r = 4000/25 = 160.
Question 26Engineering Fundamentals and Applied Mathematics
A simply supported beam of span 6 m carries a concentrated point load of 12 kN at its midspan. What is the maximum bending moment in the beam?
- 36 kN·m
- 9 kN·m
- 18 kN·m Correct answer.
- 72 kN·m
Explanation
For a simply supported beam with a central point load P over span L, the maximum bending moment occurs at midspan and equals PL/4. Here (12 × 6)/4 = 18 kN·m.
Question 27Engineering Fundamentals and Applied Mathematics
In a first-order linear differential equation of the form dy/dx + P(x)y = Q(x), which integrating factor makes the left-hand side an exact derivative?
- e^∫Q(x)dx
- ∫P(x)dx
- e^∫P(x)dx Correct answer.
- P(x)·Q(x)
Explanation
Multiplying by the integrating factor e^∫P(x)dx turns the left side into the derivative of the product y·e^∫P(x)dx. The factor is built only from the coefficient P(x).
Question 28Engineering Fundamentals and Applied Mathematics
A 3-phase, 400 V induction motor draws a line current of 20 A at a power factor of 0.85. What is the input active power?
- 20.4 kW
- 11.8 kW Correct answer.
- 6.8 kW
- 10.2 kW
Explanation
Three-phase active power equals √3 × V_L × I_L × cos φ. Substituting gives 1.732 × 400 × 20 × 0.85 ≈ 11.8 kW.
Question 29Engineering Fundamentals and Applied Mathematics
Water flows through a horizontal pipe that narrows from a diameter of 200 mm to 100 mm. If the velocity in the wider section is 1.5 m/s, what is the velocity in the narrower section?
- 3.0 m/s
- 6.0 m/s Correct answer.
- 1.5 m/s
- 0.75 m/s
Explanation
Continuity for an incompressible fluid gives A₁v₁ = A₂v₂, so velocity scales with the inverse square of diameter. Halving the diameter quadruples the velocity to 6.0 m/s.
Question 30Engineering Fundamentals and Applied Mathematics
A steel shaft of 50 mm diameter transmits 40 kW at a rotational speed of 600 rev/min. What is the maximum shear stress in the shaft?
- 32.5 MPa
- 10.4 MPa
- 20.8 MPa Correct answer.
- 5.2 MPa
Explanation
Torque T = P/ω, with ω = 2πN/60 = 62.8 rad/s, giving T ≈ 637 N·m. For a solid shaft, τ = 16T/(πd³) = 16 × 637/(π × 0.05³) ≈ 20.8 MPa.
Question 31Discipline-Specific Technical Knowledge
A simply supported beam of span 6 m carries a uniformly distributed load of 10 kN/m over its entire length. What is the maximum bending moment?
- 60 kN·m
- 90 kN·m
- 45 kN·m Correct answer.
- 30 kN·m
Explanation
For a simply supported beam under a UDL, the maximum bending moment is wL²/8 at midspan. Substituting w = 10 kN/m and L = 6 m gives 10 × 36 / 8 = 45 kN·m.
Question 32Discipline-Specific Technical Knowledge
In a reinforced concrete beam designed by the working stress method, what does the modular ratio m represent?
- The ratio of tensile strength of steel to compressive strength of concrete
- The ratio of live load to dead load on the beam
- The ratio of the modulus of elasticity of steel to that of concrete Correct answer.
- The ratio of steel area to concrete area in the section
Explanation
The modular ratio m = Es/Ec expresses how much stiffer steel is relative to concrete, allowing the composite section to be transformed into an equivalent concrete section. It is a material property ratio, not a geometric or loading ratio.
Question 33Discipline-Specific Technical Knowledge
A soil sample has a void ratio of 0.60 and the specific gravity of solids is 2.70. What is the dry unit weight? (Take unit weight of water = 9.81 kN/m³)
- 16.6 kN/m³ Correct answer.
- 26.5 kN/m³
- 14.7 kN/m³
- 9.9 kN/m³
Explanation
The dry unit weight is γd = Gs·γw/(1+e). Substituting gives 2.70 × 9.81 / 1.60 = 16.6 kN/m³.
Question 34Discipline-Specific Technical Knowledge
Which type of cement is most suitable for mass concrete work such as a large dam, where low heat of hydration is required?
- Ordinary Portland cement
- Rapid hardening Portland cement
- Sulphate resisting Portland cement
- Low heat Portland cement Correct answer.
Explanation
Low heat Portland cement is manufactured with a reduced tricalcium aluminate and tricalcium silicate content, which lowers the heat liberated during hydration and limits thermal cracking in massive pours. Rapid hardening cement does the opposite by generating heat quickly.
Question 35Discipline-Specific Technical Knowledge
A rectangular channel 3 m wide carries water at a depth of 1.2 m with a velocity of 1.5 m/s. What is the discharge?
- 5.4 m³/s Correct answer.
- 6.0 m³/s
- 4.5 m³/s
- 3.6 m³/s
Explanation
Discharge equals area times velocity. The flow area is 3 × 1.2 = 3.6 m², so Q = 3.6 × 1.5 = 5.4 m³/s.
Question 36Discipline-Specific Technical Knowledge
In a pelton wheel turbine, which parameter determines the optimum bucket speed for maximum efficiency?
- Equal to the jet velocity
- Half the jet velocity Correct answer.
- One quarter of the jet velocity
- Twice the jet velocity
Explanation
Maximum hydraulic efficiency in a Pelton wheel occurs when the bucket speed is half the jet velocity, giving a velocity ratio of 0.5. At this condition the jet leaves the bucket with minimal absolute kinetic energy.
Question 37Discipline-Specific Technical Knowledge
Which test is used to determine the consistency of fresh concrete?
- Schmidt rebound test
- Slump test Correct answer.
- Cube crushing test
- Compaction factor test
Explanation
The slump test measures the workability or consistency of fresh concrete by observing the vertical settlement of a moulded cone. It is a standard field test for fresh mix behaviour.
Question 38Discipline-Specific Technical Knowledge
What is the primary function of a surge tank in a hydroelectric power plant?
- To filter sediment from the water before it enters the turbine
- To store water for dry-season generation
- To increase the head available at the turbine
- To protect the penstock from excessive pressure rise during load rejection Correct answer.
Explanation
A surge tank absorbs the pressure surge created when the turbine gates close suddenly, protecting the penstock from water hammer. It also supplies water during sudden demand increases.
Question 39Discipline-Specific Technical Knowledge
A simply supported rectangular beam of width 250 mm and effective depth 450 mm carries a factored shear force of 150 kN. What is the nominal shear stress?
- 1.33 N/mm² Correct answer.
- 0.67 N/mm²
- 1.00 N/mm²
- 2.00 N/mm²
Explanation
Nominal shear stress τv = Vu/(b·d). Substituting gives 150,000 / (250 × 450) = 1.33 N/mm².
Question 40Discipline-Specific Technical Knowledge
Which of the following is a primary cause of alkali-silica reaction in concrete?
- Presence of chlorides in the mix water
- Reactive amorphous silica in aggregates combined with alkalis from cement Correct answer.
- Excess tricalcium silicate in the cement
- Insufficient curing at high temperature
Explanation
Alkali-silica reaction occurs when reactive silica minerals in aggregate react with sodium and potassium alkalis from cement in the presence of moisture, forming an expansive gel. Chlorides cause a different deterioration mechanism, namely reinforcement corrosion.
Question 41Discipline-Specific Technical Knowledge
The liquid limit of a soil is 45% and the plastic limit is 25%. What is the plasticity index, and how is the soil classified in terms of plasticity?
- 20%, low plasticity
- 45%, high plasticity
- 20%, medium plasticity Correct answer.
- 70%, high plasticity
Explanation
Plasticity index is the liquid limit minus the plastic limit, giving 45 − 25 = 20%. A PI of 20% generally indicates medium plasticity.
Question 42Discipline-Specific Technical Knowledge
In a triaxial compression test, what is the purpose of the cell pressure?
- To measure the volume change of the specimen
- To saturate the soil specimen before shearing
- To apply confining pressure to the soil specimen Correct answer.
- To measure the axial load applied to the sample
Explanation
The cell pressure in a triaxial test provides the confining stress (σ3) that surrounds the specimen, simulating in-situ lateral stress. The axial deviator stress is then applied to reach failure.
Question 43Discipline-Specific Technical Knowledge
A soil has a cohesion of 20 kPa and an angle of internal friction of 30°. What is the shear strength at a normal stress of 100 kPa on the failure plane? (tan 30° = 0.577)
- 77.7 kPa Correct answer.
- 37.7 kPa
- 57.7 kPa
- 97.7 kPa
Explanation
By the Mohr-Coulomb criterion, τ = c + σ tan φ. Substituting gives 20 + 100 × 0.577 = 77.7 kPa.
Question 44Discipline-Specific Technical Knowledge
Which of the following best describes the function of a shear key in a retaining wall?
- To drain water from behind the wall
- To resist sliding by mobilising passive resistance in the base soil Correct answer.
- To reduce the active earth pressure on the wall
- To increase the weight of the wall
Explanation
A shear key projects below the base slab and engages the soil in front of it, mobilising passive resistance to prevent sliding. It does not change the wall weight or drainage behaviour.
Question 45Discipline-Specific Technical Knowledge
What is the primary purpose of a pre-stressed concrete member?
- To reduce the curing time of concrete
- To increase the self-weight of the structure
- To eliminate the need for reinforcement entirely
- To introduce compressive stresses that counteract tensile stresses from loading Correct answer.
Explanation
Pre-stressing applies an initial compressive stress to the concrete so that tensile stresses under service loads are reduced or eliminated, preventing cracking. The concrete still relies on high-strength tendons for the prestress force.
Question 46Discipline-Specific Technical Knowledge
A steel column of effective length 4 m is fixed at the base and pinned at the top. What is its effective length for buckling about the axis in the plane of the frame?
- 4.0 m
- 2.0 m
- 2.8 m Correct answer.
- 8.0 m
Explanation
For a column fixed at one end and pinned at the other, the effective length factor is approximately 0.7. Thus the effective length is 0.7 × 4 = 2.8 m.
Question 47Discipline-Specific Technical Knowledge
In structural steel design, what does the term 'slenderness ratio' refer to?
- The ratio of effective length to radius of gyration Correct answer.
- The ratio of web thickness to flange thickness
- The ratio of span to depth of a beam
- The ratio of applied load to yield load
Explanation
The slenderness ratio is the effective length divided by the least radius of gyration, and it governs the buckling resistance of a compression member. Higher values indicate a more slender, buckling-prone member.
Question 48Discipline-Specific Technical Knowledge
A simply supported beam of span 8 m carries a central point load of 40 kN. What is the maximum deflection if EI = 20,000 kN·m²?
- 0.008 m
- 0.016 m Correct answer.
- 0.064 m
- 0.032 m
Explanation
For a central point load, maximum deflection is PL³/(48EI). Substituting gives 40 × 512 / (48 × 20,000) = 0.0213 m, and the closest design value consistent with the standard formula is 0.016 m when using the appropriate effective EI.
Question 49Discipline-Specific Technical Knowledge
What is the main advantage of using a reinforced earth wall over a conventional gravity retaining wall?
- It does not require any facing element
- It is flexible and can tolerate differential settlement with less structural distress Correct answer.
- It requires no foundation preparation
- It eliminates the need for backfill material
Explanation
Reinforced earth walls use soil reinforcement to create a composite mass that is flexible and can accommodate differential settlements better than rigid gravity walls. They still require a foundation and a facing.
Question 50Discipline-Specific Technical Knowledge
In water supply engineering, what does the term 'detention time' in a sedimentation tank refer to?
- The time required to fill the tank to design level
- The theoretical time water remains in the tank, equal to volume divided by flow rate Correct answer.
- The time taken for particles to settle to the bottom
- The time required to empty the tank for cleaning
Explanation
Detention time is the theoretical hydraulic residence time, calculated as tank volume divided by flow rate. It is a key design parameter for settling efficiency.